Original title Corps Locaux Publication date 1980 Pages 241 pp. Subject Algebraic number theory | Country France Media type Print Originally published 1980 Genre Non-fiction OCLC 4933106 | |
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Publisher Springer Science+Business Media Similar 局部域, A Course in Arithmetic, Graduate Texts in Mathematics | ||
Corps Locaux by Jean-Pierre Serre, originally published in 1962 and translated into English as Local Fields by Marvin Jay Greenberg in 1979, is a seminal graduate-level algebraic number theory text covering local fields, ramification, group cohomology, and local class field theory. The book's end goal is to present local class field theory from the cohomological point of view. This theory concerns extensions of "local" (i.e., complete for a discrete valuation) fields with finite residue field.
Contents
- Part I, Local Fields (Basic Facts): Discrete valuation rings, Dedekind domains, and Completion.
- Part II, Ramification: Discriminant & Different, Ramification Groups, The Norm, and Artin Representation.
- Part III, Group Cohomology: Abelian & Nonabelian Cohomology, Cohomology of Finite Groups, Theorems of Tate and Nakayama, Galois Cohomology, Class Formations, and Computation of Cup Products.
- Part IV, Local Class Field Theory: Brauer Group of a Local Field, Local Class Field Theory, Local Symbols and Existence Theorem, and Ramification.
References
Local Fields Wikipedia(Text) CC BY-SA